63,627 research outputs found
Constructive Field Theory and Applications: Perspectives and Open Problems
In this paper we review many interesting open problems in mathematical
physics which may be attacked with the help of tools from constructive field
theory. They could give work for future mathematical physicists trained with
the constructive methods well within the 21st century
Simplified models of electromagnetic and gravitational radiation damping
In previous work the authors analysed the global properties of an approximate
model of radiation damping for charged particles. This work is put into context
and related to the original motivation of understanding approximations used in
the study of gravitational radiation damping. It is examined to what extent the
results obtained previously depend on the particular model chosen. Comparisons
are made with other models for gravitational and electromagnetic fields. The
relation of the kinetic model for which theorems were proved to certain
many-particle models with radiation damping is exhibited
Diffuse-Charge Dynamics in Electrochemical Systems
The response of a model micro-electrochemical system to a time-dependent
applied voltage is analyzed. The article begins with a fresh historical review
including electrochemistry, colloidal science, and microfluidics. The model
problem consists of a symmetric binary electrolyte between parallel-plate,
blocking electrodes which suddenly apply a voltage. Compact Stern layers on the
electrodes are also taken into account. The Nernst-Planck-Poisson equations are
first linearized and solved by Laplace transforms for small voltages, and
numerical solutions are obtained for large voltages. The ``weakly nonlinear''
limit of thin double layers is then analyzed by matched asymptotic expansions
in the small parameter , where is the
screening length and the electrode separation. At leading order, the system
initially behaves like an RC circuit with a response time of
(not ), where is the ionic diffusivity, but nonlinearity
violates this common picture and introduce multiple time scales. The charging
process slows down, and neutral-salt adsorption by the diffuse part of the
double layer couples to bulk diffusion at the time scale, . In the
``strongly nonlinear'' regime (controlled by a dimensionless parameter
resembling the Dukhin number), this effect produces bulk concentration
gradients, and, at very large voltages, transient space charge. The article
concludes with an overview of more general situations involving surface
conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference
Applications of the Mellin-Barnes integral representation
We apply the Mellin-Barnes integral representation to several situations of
interest in mathematical-physics. At the purely mathematical level, we derive
useful asymptotic expansions of different zeta-functions and partition
functions. These results are then employed in different topics of quantum field
theory, which include the high-temperature expansion of the free energy of a
scalar field in ultrastatic curved spacetime, the asymptotics of the -brane
density of states, and an explicit approach to the asymptotics of the
determinants that appear in string theory.Comment: 20 pages, LaTe
Quantum gravity at a large number of dimensions
We consider the large- limit of Einstein gravity. It is observed that a
consistent leading large- graph limit exists, and that it is built up by a
subclass of planar diagrams. The graphs in the effective field theory extension
of Einstein gravity are investigated in the same context, and it is seen that
an effective field theory extension of the basic Einstein-Hilbert theory will
not upset the latter leading large- graph limit, {\it i.e.}, the same
subclass of planar diagrams will dominate at large- in the effective field
theory. The effective field theory description of large- quantum gravity
limit will be renormalizable, and the resulting theory will thus be completely
well defined up to the Planck scale at GeV. The
expansion in gravity is compared to the successful expansion in
gauge theory (the planar diagram limit), and dissimilarities and parallels of
the two expansions are discussed. We consider the expansion of the effective
field theory terms and we make some remarks on explicit calculations of
-point functions.Comment: 18 pages, 23 figures (75 files), format RevTex4, typos corrected,
references adde
On two aspects of the Painleve analysis
We use the Calogero equation to illustrate the following two aspects of the
Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the
Painleve test for integrability, the singular expansions of its solutions
around characteristic hypersurfaces can be neither single-valued functions of
independent variables nor single-valued functionals of data. Second, if the
truncation of singular expansions of solutions is consistent, the truncation
not necessarily leads to the simplest, or elementary, auto-Backlund
transformation related to the Lax pair.Comment: 8 page
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